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LESSON: Adding and Subtracting Fractions with Like Denominators

Site: MN Partnership for Collaborative Curriculum
Course: Mathematics Essentials Q1
Book: LESSON: Adding and Subtracting Fractions with Like Denominators
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Date: Sunday, November 24, 2024, 11:09 PM

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LESSON: Adding and Subtracting Fractions with Like Denominators

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READ: Add Fractions with Like Denominators

Add Fractions With Like Denominators

You have already learned how to add whole numbers and how to add decimals, now you are going to learn how to add fractions. In this lesson, you will learn all about adding fractions with like or common denominators.

What is a like denominator? A like denominator is a denominator that is the same. This means that the whole has been divided up into the same number of parts. If the denominator of two fractions is a five, then both of those fractions have been divided into five parts. The numerators may be different, but the denominators are the same.

This picture shows two different fractions with like denominators.

Now let’s say that we want to add these two fractions. Because the denominators are common, we are adding like parts. We can simply add the numerators and we will have our new fraction.

\frac{2}{6} + \frac{4}{6} = \frac{6}{6}

Here it is as a picture.

We combined both of these fractions together to have a fraction we can call six-sixths. What about simplifying? We must simplify or reduce all of our answers. In this example, when we have six out of six parts, we have one whole. You can see that one whole figure is shaded in. We simplify our answer and then our work is complete.

Our final answer is \frac{6}{6} = 1.


Let’s look at another one. We can work on this one without looking at a picture.

Example

\frac{2}{8} + \frac{4}{8} = \underline{\;\;\;\;\;\;\;\;\;}

The first step is to check and be sure that you have like denominators. In this example, both denominators are 8, so we can add the numerators because the denominators are alike.

Our next step is to add the numerators.

2 + 4 = 6

We put that number over the common denominator.

\frac{6}{8}

Our last step is to check and see if we can simplify our answer. In this example, 6 and 8 have the greatest common factor of 2. We divide both the numerator and the denominator by 2 to simplify the fraction.

\frac{6 \div 2}{8 \div 2} = \frac{3}{4}

Our final answer is \frac{3}{4}.

READ: Subtract Fractions with Like Denominators

Subtract Fractions with Like Denominators

We can also subtract fractions with like denominators to find the difference between the fractions. As long as the denominators are the same, the fractions are alike, and we can simply subtract the numerators.

Here is an example done with pictures.

\frac{6}{8} - \frac{3}{8} = \underline{\;\;\;\;\;\;\;\;\;}

To solve this problem, we simply subtract the parts or the numerators. The difference between six and three is three. Then we put that answer over the common denominator.

Our final answer is \frac{3}{8}.

We don’t need to simplify this fraction because three-eighths is already in simplest form

READ: Adding & Subtracting Mixed Numbers with Like Denominators

Adding and Subtracting Mixed Numbers with Like Denominators

Do you remember what a mixed number is? A mixed number has both whole quantities and parts. Said another way, a mixed number has a whole number and a fraction with it.

9\frac{4}{5} is a mixed number. It has nine wholes and four-fifths of another whole.


Adding mixed numbers is a lot like adding fractions, the key is that you have to add the fraction parts before you add the whole numbers. If you think about this it makes perfect sense. Sometimes, we can add two fractions and get a whole number. We always want to make sure that we have considered this possibility first, that is why you add the fractions before you add the whole numbers.

Here is an example where the sum of two fractions equals a whole number.

Example

\frac{4}{6}+\frac{2}{6}=\frac{6}{6}=1

Here the two fractions added together equal one whole.

When we are adding two mixed numbers with common denominators, we add the fractions first and then the whole numbers.

Example

& \quad \ \ \ 6\frac{1}{4}\\ &\underline{+ \ \quad 3\frac{2}{4}\;}\\ & \qquad 9\frac{3}{4}

First, we added the fractions. One-fourth plus two-fourths is equal to three-fourths. Then we added the whole numbers. Six plus three is equal to nine. Our answer is nine and three-fourths. Our fraction is in simplest form, so our work is done. Always be sure your answer is in the simplest form!


Example

& \quad \ \ 5\frac{2}{5}\\ & \underline{+ \quad 3\frac{3}{5}\;}\\ & \ \qquad 9

When we start this problem by adding the fractions, we end up with five-fifths which is the same as one whole. We need to add that one whole to the sum of 5 and 3.

Our final answer is 9.


Just as we can add mixed numbers, we can also subtract mixed numbers. The same rule applies, always subtract the fraction parts first then the whole numbers.

Example

& \quad \ \ 6\frac{3}{8}\\ & \underline{- \quad 4\frac{1}{8}\;}

We start by subtracting the fractions first, and these fractions have the same denominator so we can simply subtract the numerators.

Three-eighths take away one-eighth is two-eighths.

\frac{3}{8}-\frac{1}{8}=\frac{2}{8}

Next, we subtract the whole numbers. 6 - 4 is 2.

Our answer is 2\frac{2}{8}.

However, our work is not finished because we can simplify two-eighths.

\frac{2}{8}=\frac{1}{4}

Our final answer is 2\frac{1}{4}.

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

CHECK Yourself! Adding and Subtracting Fractions with Like Denominators

Go to the VoiceThread linked below for this Self Check Quiz! Following each question, the correct answer is given. Remember, this is a chance for you to see how you are doing with the content before being graded on it. Please ask for help if you need it!

Click Here for the Self Check Quiz VoiceThread